MathDB

In the triangle

ABC

on the side

BC

, the points

D

and

E

are chosen so that the angle

BAD

is equal to the angle

EAC

. Let

I

and

J

be the centers of the inscribed circles of triangles

ABD

and

AEC

respectively,

F

be the point of intersection of

BI

and

EJ

G

be the point of intersection of

DI

and

CJ

. Prove that the points

I, J, F, G

lie on one circle, the center of which belongs to the line

I_bI_c

, where

I_b

and

I_c

are the centers of the exscribed circles of the triangle

ABC

, which touch respectively sides

AC

and

AB

2020.13